This will depend a lot on which editor you use and the features it provides so I doubt there will be a single answer; however, if you editor has good regex support then this should be pretty easy.
Here's how you can match for $...$
/\s\$(.|\n)+?\$/g
and similarly, matching for $$...$$:
/\s\$\$(.|\n)+?\$\$/g
This will not match the dollar signs as they have to be escaped with \$ and the above pattern requires any of the whitespace characters before the dollar sign (space, tab or newline). You can see a nice visualization for that here and here respectively.
If your editor supports the s flag from Perl, then you can simplify (.|\n)+? to just .+? as . will match new lines too.
Finally, putting it together with a substitution, you get:
s/(\s)\$(.+?)\$/\1\(\2\)/sg
Note that I'm not escaping certain characters because it will depend on the particular implementation of regex. In particular, the group parentheses may require \(...\) and the +, ? and the backslashes in the replacement may also need to be escaped depending on which regex implementation you are using.
If you are in the command line and have Perl, then the following two commands should do the trick:
perl -077pi.bak -e 's/(\s)\$\$(.+?)\$\$/\1\\[\2\\]/sg' document.tex
perl -077pi.bak -e 's/(\s)\$(.+?)\$/\1\\(\2\\)/sg' document.tex
Note that this will not match anything at the very start of the file; however, I don't think this will be a big issue as the start of the file will typically be a comment or at least \documentclass.
\( .. \)right now, you can live with$..$. About the display math with a basic regular expressions it could work, search\$\$([\s\S]+?)\$\$and replace\[\1\]. – Manuel Feb 16 '16 at 23:40sed... – cfr Feb 17 '16 at 01:09$$...$$has been deprecated for 20+ years. If nothing terrible has happened by now, it isn't likely to do so tomorrow. Just start using the new syntax as you edit ($...$is OK.) – cfr Feb 17 '16 at 01:14sedwould be at all happy. – cfr Feb 17 '16 at 01:25